TR-2001-02

On decomposing a hypergraph into k connected sub-hypergraphs

Abstract

We extend first the notion of graphic matroids for
hypergraphs and apply then the matroid partition theorem of Edmonds to
obtain a generalization of Tutte's disjoint trees theorem for
hypergraphs. As a corollary, we prove for positive integers k and q that
every (kq)-edge-connected hypergraph of rank q can be
decomposed into k connected sub-hypergraphs, a well-known result for
q=2. Another by-product is a sufficient condition for the existence
of k edge-disjoint Steiner trees in a bipartite graph.